# Solving a trig equation

• Dec 9th 2009, 06:45 PM
>_<SHY_GUY>_<
Solving a trig equation
Can someone please help me with this problem? Thank you:)

If possible, find the exact solutions algebraically

(sin2x + cos2x)^2 =1
• Dec 9th 2009, 06:53 PM
mr fantastic
Quote:

Originally Posted by >_<SHY_GUY>_<
Can someone please help me with this problem? Thank you:)

If possible, find the exact solutions algebraically

(sin2x + cos2x)^2 =1

Expand the left hand side and apply the Pythagorean Identity. After simplifying, the equation becomes $\displaystyle 2 \sin (2x) \cos (2x) = 0$ which can be easily solved in a number of ways.
• Dec 9th 2009, 06:55 PM
11rdc11
Quote:

Originally Posted by >_<SHY_GUY>_<
Can someone please help me with this problem? Thank you:)

If possible, find the exact solutions algebraically

(sin2x + cos2x)^2 =1

yes make the sub u =2x

The equation then turns into

$\displaystyle (\sin{u} +\cos{u})^2 =1$
• Dec 9th 2009, 07:08 PM
NOX Andrew
I have removed my method since the method submitted by mr fantastic is much more efficient than mine. (Doh)